Explore Reasons Behind Dramatic Difference between AQI’s by U.S. and Chinese government

author: Li Luo, Zhuangye Chen date: 02/10/2016 font-family: ‘Helvetica’

Overview

Background

How is Air Quality Index (AQI) calculated?

\[ IAQI_p = \frac{I_{high} - I_{low}}{C_{high} - C_{low}} (C - C_{low}) + I_{low} \] \(C\) = the pollutant concentration
\(C_{low}\)= the concentration breakpoint that is \(\le C\)
\(C_{high}\)= the concentration breakpoint that is \(\ge C\)
\(I_{low}\)= the index breakpoint corresponding to \(C_{low}\)
\(I_{high}\)= the index breakpoint corresponding to \(C_{high}\)

Different Breakpoints

PM2.5 (\(\mu g/m^3\)) AQI by China AQI by U.S.
0 0 0
10 14.3 32
30 42.9 87
50 68.8 125
70 93.8 154
90 118.8 165
100 131.3 171
120 157.1 182
150 200.0 200
170 220.0 220
200 250.0 250
300 350.0 350

Adjustment Based On Breakpoints

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\[ {\tiny AQI_{U.S.} = 2.54\times 10^{-5} AQI_{China}^3 - 1.31\times 10^{-2} AQI_{China}^2 + 2.59 AQI_{China} } \]

10 Biggest AQI Difference In Photos

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Stationary Test

In order to see if the difference in AQI reported by China and U.S. exsits, we check the stationarity of this time series with ADF test.

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Stationary Test Result

zeromean <- aqidiff$aqi_diff-mean(aqidiff$aqi_diff)
library(tseries)
pvalue <- adf.test(zeromean)$p.value
pvalue
[1] 0.01

The test shows the data is stationary. Taking into account of difference average 12.1317722, we can conclude that the difference of AQI reported by China and US really exists.

Seasonal Trend Decomposition

aqidiff.ts<-ts(aqidiff$aqi_diff,frequency=365)
aqidiff.de<-decompose(aqidiff.ts,type="additive")
plot(aqidiff.de)

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